Swab mops having mop heads made of yarn, cotton, or similar cloth-type strands are commonly used to clean soiled surfaces and to absorb moisture from wet surfaces. Of course during use, these mop heads become soiled and, after prolonged use, become worn and are no longer effective in cleaning operations, and the mop heads and mops on which they are mounted must be discarded. As a result, mops with removable mop heads are popular, in that when a mop head becomes unusable, it can be removed and replaced with a new mop head, thus preventing the entire mop from being discarded. To accomplish this, mop head holders or retaining clamps are used for removeably retaining mop heads on mop handles. However, no retaining device has been developed which truly securely maintains a mop head on its mop and which easily and readily allows the user to replace an old mop head with a new one, without difficulty and without the mess associated with removing an old, soiled and often wet mop head.